Collider experiments will achieve percent level precision measurements of several processes key to answer some of the most pressing questions of contemporary particle physics. In this talk I will show that the capability to predict and describe such observables at next-to-next-to-next-to-leading order (N3LO) in QCD perturbation theory is crucial to fully exploit these experimental measurements.
I will describe how to compute differential distributions via slicing methods and illustrate the calculation of the N3LO TMD beam functions, the last missing ingredient for extending these techniques to N3LO.
Finally, I will present our new determination of the rapidity anomalous dimension (Collins-Soper kernel) to N4LO and employ it to carry out the resummation of the Energy-Energy Correlation at N4LL, the first resummation for an event shape at this level of accuracy.